Question

Find the average rate of change of the function f(x)=(1/x-7) as x changes from x=-2 to x=5

Answer 1

Answer:

$-\frac{1}{18}$

Step-by-step explanation:

Average rate of change = $\frac{f(b) - f(a)}{b - a}$

Where,

a = -2,

f(a) = f(-2) = $\frac{1}{(-2) - 7} = \frac{1}{-9}$ = -⅑

f(a) = -⅑

b = 5

f(b) = f(5) = $\frac{1}{(5) - 7} = \frac{1}{-2}$ = -½

f(b) = -½

Plug in the values into the equation

Average rate of change = $\frac{-\frac{1}{2} - (-\frac{1}{9}}{5 -(-2)}$

$= \frac{\frac{-9 - (-2)}{18}}{7}$

$= \frac{\frac{-7}{18}}{7}$

$= \frac{-7}{18} * \frac{1}{7}$

$= \frac{-1}{18} * \frac{1}{1}$

$= \frac{-1}{18} * 1$

$= -\frac{1}{18}$